Abstract
Transient anomalous diffusion may be modeled by a tempered fractional diffusion equation. A reflecting boundary condition enforces mass conservation on a bounded interval. In this work, explicit and implicit Euler schemes for tempered fractional diffusion with discrete reflecting or absorbing boundary conditions are constructed. Discrete reflecting boundaries are formulated such that the Euler schemes conserve mass. Conditional stability of the explicit Euler methods and unconditional stability of the implicit Euler methods are established. Analytical steady-state solutions involving the Mittag-Leffler function are derived and shown to be consistent with late-time numerical solutions. Several numerical examples are presented to demonstrate the accuracy and usefulness of the proposed numerical schemes.
This paper is dedicated to the memory of late Professor Wen Chen
Acknowledgments
We would like to thank Harish Sankanarayanan (Department of Statistics and Probability, Michigan State University) for the fruitful discussions and suggestions for improving the manuscript. This work was supported by the OSD/ARO/MURI on “Fractional PDEs for Conservation Laws and Beyond: Theory, Numerics and Applications” (W911NF-15-1-0562). Kelly acknowledges support of the Chief of Naval Research via the base 6.1 support program.
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© 2019 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA special issue – In memory of late professor Wen Chen (FCAA–Volume 22–6–2019)
- Survey Paper
- State-of-art survey of fractional order modeling and estimation methods for lithium-ion batteries
- An investigation on continuous time random walk model for bedload transport
- Tutorial Survey
- Porous functions
- Research Paper
- A time-space Hausdorff derivative model for anomalous transport in porous media
- High-order algorithms for riesz derivative and their applications (IV)
- Mass-conserving tempered fractional diffusion in a bounded interval
- Dispersion analysis for wave equations with fractional Laplacian loss operators
- Lagrangian solver for vector fractional diffusion in bounded anisotropic aquifers: Development and application
- Some further results of the laplace transform for variable–order fractional difference equations
- Robust stability analysis of LTI systems with fractional degree generalized frequency variables
- Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA special issue – In memory of late professor Wen Chen (FCAA–Volume 22–6–2019)
- Survey Paper
- State-of-art survey of fractional order modeling and estimation methods for lithium-ion batteries
- An investigation on continuous time random walk model for bedload transport
- Tutorial Survey
- Porous functions
- Research Paper
- A time-space Hausdorff derivative model for anomalous transport in porous media
- High-order algorithms for riesz derivative and their applications (IV)
- Mass-conserving tempered fractional diffusion in a bounded interval
- Dispersion analysis for wave equations with fractional Laplacian loss operators
- Lagrangian solver for vector fractional diffusion in bounded anisotropic aquifers: Development and application
- Some further results of the laplace transform for variable–order fractional difference equations
- Robust stability analysis of LTI systems with fractional degree generalized frequency variables
- Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network